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Exercise Mathemtics Form 4

Bab 07 – PROBABILITY I

Chapter 07 – KEBARANGKALIAN I

JAWAPAN / ANSWER

Question: http://goo.gl/AwxcsW

EXERCISE 1

1) {1, 2, 3, 4, 5, 6}

(a) {1, 3, 5}

(b) {3, 6}

2) {N, E, R, 2, 9, 3, 8}

(a) Set P {𝑵𝑵,𝑬𝑬,𝑹𝑹}.

(b) Set Q {𝑵𝑵,𝑹𝑹,𝟗𝟗,𝟑𝟑}.

3) {𝑃𝑃,𝑅𝑅,𝑂𝑂,𝐵𝐵,𝐴𝐴,𝐵𝐵, 𝐼𝐼, 𝐿𝐿, 𝐼𝐼,𝑇𝑇,𝑌𝑌}

Elements {𝑃𝑃,𝑅𝑅,𝑂𝑂,𝐵𝐵,𝐴𝐴, 𝐼𝐼, 𝐿𝐿,𝑇𝑇,𝑌𝑌} = 9 elements

4) Coins {𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻,𝑇𝑇𝐻𝐻𝑇𝑇𝑇𝑇}

(a) {(𝑯𝑯𝑯𝑯𝑯𝑯𝑯𝑯,𝑯𝑯𝑯𝑯𝑯𝑯𝑯𝑯), (𝑻𝑻𝑯𝑯𝑻𝑻𝑻𝑻,𝑻𝑻𝑯𝑯𝑻𝑻𝑻𝑻)}

(b) {(𝑯𝑯𝑯𝑯𝑯𝑯𝑯𝑯,𝑻𝑻𝑯𝑯𝑻𝑻𝑻𝑻), (𝑻𝑻𝑯𝑯𝑻𝑻𝑻𝑻,𝑯𝑯𝑯𝑯𝑯𝑯𝑯𝑯)}

5) _ 8𝑥𝑥

=27

𝑥𝑥 =72

× 8

𝒙𝒙 = 𝟐𝟐𝟐𝟐

ANSWER / JAWAPAN CHAPTER 07 – PROBABILITY I (MATHEMATICS FORM 4) BAB 06 – KEBARANGKALIAN I (MATEMATIK TINGKATAN 4) © HAK CIPTA TERPELIHARA JAN 2015 https://tutormansor.wordpress.com/

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http://goo.gl/AwxcsW


6) _ 25

× 365 = 𝟏𝟏𝟏𝟏𝟏𝟏 𝐻𝐻𝐻𝐻𝑑𝑑𝑑𝑑

7) Hari Raya Cards

Family = 5, Relatives = 10, Friends = 15

Total = 30

(a) Send by family

530

=𝟏𝟏𝟏𝟏

(b) Not sent by her relatives

5 + 1530

=2030

=𝟐𝟐𝟑𝟑

8) Probability for red marble 120280

=𝟑𝟑𝟕𝟕

Probability of green marble 14

=𝑥𝑥

280

𝑥𝑥 =14

× 280

= 70

Probability for white marbles

1 −14−

37

=9

28

White marbles 𝑑𝑑

280=

928

𝑑𝑑 =9

28× 280

= 90


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9) Girl = 80, Boy = 115 − 80 = 35

After, Boy = 35 + 5 = 40

Probability

40115 + 5

=𝟏𝟏𝟑𝟑

10) Red = 75, Green = 90, Blue = 𝑥𝑥.

(a) Red 14

=75

75 + 90 + 𝑥𝑥

=75

165 + 𝑥𝑥

165 + 𝑥𝑥 = 75(4)

165 + 𝑥𝑥 = 300

𝑥𝑥 = 300 − 165

= 𝟏𝟏𝟑𝟑𝟏𝟏

(b) If the number of student is small, the probability still same. Probability for green 90

75 + 90 + 135=

90300

=3

10

No of student from 100 3

10× 100 = 30 students


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Exercise 2

1) Blue balls = 3, white balls = 4, green balls = 2

3 elements

2) {𝑂𝑂,𝐴𝐴, 𝐼𝐼}

3) All the possible outcomes

{(𝐻𝐻,𝐻𝐻,𝐻𝐻), (𝑇𝑇,𝐻𝐻,𝐻𝐻), (𝐻𝐻,𝑇𝑇,𝐻𝐻), (𝐻𝐻,𝐻𝐻,𝑇𝑇), (𝐻𝐻,𝑇𝑇,𝑇𝑇), (𝑇𝑇,𝐻𝐻,𝑇𝑇), (𝑇𝑇,𝑇𝑇,𝐻𝐻), (𝑇𝑇,𝑇𝑇,𝑇𝑇)}

Anwers : {(𝑻𝑻,𝑯𝑯,𝑯𝑯), (𝑯𝑯,𝑻𝑻,𝑯𝑯), (𝑯𝑯,𝑯𝑯,𝑻𝑻)}

4) Red = 5, Black = 7, Yellow = 3

Probability of red 5

5 + 7 + 3=

515

=13

5) 28 teams 14

× 28 = 7 teams

6) Total employees = 550 15

= 550

= 110 employees


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7) Green = 24, Blue = 𝑥𝑥

Probability green 8

10=

2424 + 𝑥𝑥

8(24 + 𝑥𝑥) = 24(10)

192 + 8𝑥𝑥 = 240

8𝑥𝑥 = 240 − 192

= 48

𝑥𝑥 =488

= 6

8) 36 numbers card

Probability of odd number

1 −16

=56

56

× 36 = 30

9) Red = 30, Black = 50, Blue = 𝑥𝑥

Probability of black pen

516

=50

30 + 50 + 𝑥𝑥

=50

80 + 𝑥𝑥

5(80 + 𝑥𝑥) = 16(50)

400 + 5𝑥𝑥 = 800

5𝑥𝑥 = 800 − 400

= 400

𝑥𝑥 =400

5

= 𝟐𝟐𝟖𝟖


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10) List number that can divide by 4 from 1 – 30 {4,8,12,16,20,24,28} 𝟕𝟕𝟑𝟑𝟖𝟖

Diagnostic Test

1) Girls = 35, Boys = 45 − 35 = 10

New, Boys = 10 + 5 = 15, Total students 45 + 5 = 50

Probability of boys student 1550

=𝟑𝟑𝟏𝟏𝟖𝟖

𝑨𝑨

2) Total = 270 (Orange, Lychee, Coffee), Orange = 48, Prob. lychee 13

𝑇𝑇𝑑𝑑𝑙𝑙ℎ𝐻𝐻𝐻𝐻, 13

× 270 = 90, Coffee = 270 − 48 − 90 = 𝟏𝟏𝟑𝟑𝟐𝟐 𝑩𝑩

3) Multiple of 4 {16, 28, 60, 84}

46

=𝟐𝟐𝟑𝟑

𝑨𝑨

4) Friends = 6, Relatives = 5, Brothers = 2

Probability not sent to her brothers

6 + 56 + 5 + 2

=𝟏𝟏𝟏𝟏𝟏𝟏𝟑𝟑

𝑫𝑫


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5) Boys = 18, Girls = 𝑘𝑘

Probability of girl

47

=𝑘𝑘

18 + 𝑘𝑘

4(18 + 𝑘𝑘) = 𝑘𝑘(7)

72 + 4𝑘𝑘 = 7𝑘𝑘

72 = 7𝑘𝑘 − 4𝑘𝑘

= 3𝑘𝑘

𝑘𝑘 =723

= 𝟐𝟐𝟏𝟏 𝑩𝑩

6) Total shirt = 20

Probability of green = 15100

15100

× 20 = 𝟑𝟑 𝑨𝑨

7) Wear watches = 15, Not Wear Watches = 𝑥𝑥

Probability of wear watches = 35

35

=15

15 + 𝑥𝑥

3(15 + 𝑥𝑥) = 15(5)

45 + 3𝑥𝑥 = 75

3𝑥𝑥 = 75 − 45

= 30

𝑥𝑥 =303

= 10

New wear watches= 15 − 3 = 12, new total = (10 + 15) − 3 = 22

Probability for wearing watch 1222

=𝟏𝟏𝟏𝟏𝟏𝟏

𝑪𝑪


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8) Red = 40, White = 𝑥𝑥

Probability of white buttons

57

=𝑥𝑥

𝑥𝑥 + 40

5(𝑥𝑥 + 40) = 𝑥𝑥(7)

5𝑥𝑥 + 200 = 7𝑥𝑥

200 = 7𝑥𝑥 − 5𝑥𝑥

= 2𝑥𝑥

𝑥𝑥 =200

2

= 𝟏𝟏𝟖𝟖𝟖𝟖 𝑩𝑩

9) Probability of Team P win 12, loss 1

2

Probability of Team Q win 27, loss 5

7

Probability for P win, Q win 12

×27

=2

14

=𝟏𝟏𝟕𝟕

𝑨𝑨

10) Total eggs = 100

Probability

𝐴𝐴 =14

,𝐵𝐵 =25

,𝐶𝐶 = 1 −14−

25

=7

20

Number of eggs of Grade C 7

20× 100 = 𝟑𝟑𝟏𝟏 𝑩𝑩


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